rain-induced turbulence and air-sea gas transfer · rain-induced turbulence and air-sea gas...

Rain-induced turbulence and air-sea gas transfer

Christopher J. Zappa,1 David T. Ho,1,2 Wade R. McGillis,1,3 Michael L. Banner,1

John W. H. Dacey,4 Larry F. Bliven,5 Barry Ma,6,7 and Jeff Nystuen6

Received 2 July 2008; revised 18 March 2009; accepted 21 April 2009; published 9 July 2009.

[1] Results from a rain and gas exchange experiment (Bio2 RainX III) at the Biosphere 2Center demonstrate that turbulence controls the enhancement of the air-sea gas transfer rate(or velocity) k during rainfall, even though profiles of the turbulent dissipation rate e arestrongly influenced by near-surface stratification. The gas transfer rate scales with e

1=4 for arange of rain rates with broad drop size distributions. The hydrodynamic measurementselucidate the mechanisms responsible for the rain-enhanced k results using SF6 tracerevasion and active controlled flux technique. High-resolution k and turbulence resultshighlight the causal relationship between rainfall, turbulence, stratification, and air-sea gasexchange. Profiles of e beneath the air-sea interface during rainfall, measured for the firsttime during a gas exchange experiment, yielded discrete values as high as 10�2 W kg�1.Stratification modifies and traps the turbulence near the surface, affecting the enhancementof the transfer velocity and also diminishing the vertical mixing of mass transported tothe air-water interface. Although the kinetic energy flux is an integral measure of theturbulent input to the system during rain events, e is the most robust response to all themodifications and transformations to the turbulent state that follows. The Craig-Bannerturbulence model, modified for rain instead of breaking wave turbulence, successfullypredicts the near-surface dissipation profile at the onset of the rain event before stratificationplays a dominant role. This result is important for predictive modeling of k as it allowsinferring the surface value of e fundamental to gas transfer.

Citation: Zappa, C. J., D. T. Ho, W. R. McGillis, M. L. Banner, J. W. H. Dacey, L. F. Bliven, B. Ma, and J. Nystuen (2009),

Rain-induced turbulence and air-sea gas transfer, J. Geophys. Res., 114, C07009, doi:10.1029/2008JC005008.

1. Introduction

[2] Atmosphere-ocean interactions play a crucial role inthe regional and global budgets of biogeochemical tracegases and in the transport of volatile pollutants. A plethoraof processes has been shown in individual studies to playvarying roles in regulating air-sea gas fluxes, which contin-ually work to adjust the balance of constituents in the upperocean. Therefore, a better understanding of mechanismscontrolling air-water gas exchange and ocean mixing isneeded to improve model predictions of the spatial variabilityof air-sea fluxes.

[3] The flux, F, of a sparingly soluble gas can be param-eterized as the product of the chemical potential gradient ofthe gas between the air and water, and the gas transfervelocity, k, which embodies the details of the turbulence-mediated transfer across the surface aqueous mass boundarylayer (MBL). The chemical potential gradient of the gas canbe defined involving a variety of expressions of solubility.The solubility of a gas also prescribes whether a gas is eitherliquid-phase or gas-phase controlled [Liss and Slater, 1974]and is also important in bubble-mediated processes [AsherandWanninkhof, 1998;Keeling, 1993;Merlivat andMemery,1983; Woolf, 1993]. Near-surface turbulence is presumed tobe the driving mechanism that regulates k across the air-waterinterface in the absence of bubbles. The magnitude of k isdetermined by the molecular diffusivity of a gas and thespatially and temporally varying MBL, whose thickness is afunction of near surface turbulence and diffusivity.[4] Wind has long been known to drive gas exchange in the

open ocean because it plays a central role in the generation ofturbulence through the transfer of momentum to waves andcurrents. As a result, numerous relationships between k andwind speed have been developed [e.g., Ho et al., 2006; Lissand Merlivat, 1986; Nightingale et al., 2000; Wanninkhof,1992; Wanninkhof and McGillis, 1999]. However, manyprocesses and mechanisms, both related and unrelated towind-forcing, havebeendetermined to influencegas exchange,including short wind waves [e.g., Bock et al., 1999; Jahne

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, C07009, doi:10.1029/2008JC005008, 2009

1Lamont-Doherty Earth Observatory, Earth Institute at Columbia Uni-versity, Palisades, New York, USA.

2Now at Department of Oceanography, University of Hawai’i at Manoa,Honolulu, Hawaii, USA.

3Department of Earth and Environmental Engineering, ColumbiaUniversity, New York, New York, USA.

4Biology Department, Woods Hole Oceanographic Institution, WoodsHole, Massachusetts, USA.

5Laboratory for Hydrospheric Processes, NASA Goddard Space FlightCenter, Wallops Island, Virginia, USA.

6Applied Physics Laboratory, University of Washington, Seattle,Washington, USA.

7Now at Electrical and Computer Engineering, Portland State University,Portland, Oregon, USA.

Copyright 2009 by the American Geophysical Union.0148-0227/09/2008JC005008

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et al., 1987], microscale wave breaking [Zappa et al., 2001,2004], bubble-mediated transfer [Asher andWanninkhof, 1998;Farmer et al., 1993; Woolf and Thorpe, 1991; Woolf, 1993],organic films [Frew, 1997; Frew et al., 2004], and rain [Hoet al., 1997, 2000]. Regardless of the specific processes and thedetails of the underlying physics, models generally attemptto parameterize k on the basis of the assumption thatturbulence regulates the exchange in the absence of bubbles.[5] The turbulence-mediated transfer across the MBL has

been explicitly related to the turbulent kinetic energy (TKE)dissipation rate, e. The resulting physical scaling relationshipfor gas transfer is

k / enð Þ1=4Sc�n; ð1Þ

where the Schmidt number, Sc, is defined as the ratio of thekinematic viscosity of water, v, to mass diffusivity D, and Scexponent n varies between 1/2 (clean surface) and 2/3 (highlycontaminated surface or rigid wall) depending on the surfaceboundary conditions [Jahne et al., 1987; Ledwell, 1984].This relationship is consistent with mass diffusion across alayer of the thickness of the Batchelor [1959] scale dB =Sc�

1=2h, where h = (n3/e)1=4 is the Kolmogorov, or dissipative,

microscale [Melville, 1996]. This expression has beenderived by Kitaigorodskii [1984] in the context of modelingthe influence of patches of enhanced turbulence by breaking.A similar scaling was developed for modeling the masstransfer of falling wavy turbulent liquid films [Banerjee et al.,1968], and has also been derived using surface renewaltheory [Lamont and Scott, 1970]. This scaling demonstratesthat increasing turbulence will enhance k, and this scaling hasbeen tested with success in laboratory grid-mixing tanks forvarying surface conditions [Asher and Pankow, 1986;Dickeyet al., 1984]. Recently, this scaling has been shown to work ina variety of environmental systems and forcings [Zappa et al.,2007] and has been suggested as a unified relationship forinterfacial fluxes at both the benthic and air-sea boundarylayers [Lorke and Peeters, 2006].[6] Raindrops falling on a freshwater surface have been

shown to enhance k in laboratory experiments and prelimi-nary field studies. These studies showed that the rain-inducedgas exchange increased with the kinetic energy flux (KEF)applied to the water surface by the raindrops [Ho et al., 1997,2000]. Ho et al. [2000] inferred that the enhancement in k byrain is dominated by the production of turbulence from theKEF of the raindrops, whereas rain-generated bubbles con-tribute 0–20% of the total gas exchange. However, the bulkKEF relationship was developed on the basis of experimentsthat were not representative of rain conditions found in naturebecause they used raindrops of discrete size. This result opensthe door for quantifying the gas transfer rate on the basis ofthe physical relationship in (1).[7] During a previous rain and gas exchange experiment at

the Biosphere 2 ocean (Bio2 RainX II), an SF6 tracer releaseexperiment was performed to quantify rain-induced gasexchange in saltwater conditions [Ho et al., 2004]. The mea-surements show the rapid depletion of SF6 in the near-surfacelayer due to rain enhancement of gas exchange, and the gastransfer velocity was similar to that in freshwater experi-ments. However, Ho et al. [2004] suggested that the near-

surface layer was not replenished as fast as it was depletedbecause rainfall in a saltwater body promotes density strat-ification of the upper water column that inhibits verticalmixing of higher-concentration SF6 from below. Therefore,the overall gas flux was lower than that found during fresh-water experiments. In addition to the SF6 evasion measure-ments, direct velocity measurements in the bulk watershowed an increase in the turbulent dissipation rate, e, duringthe rain events. This increase in e supports a link betweenturbulence and enhanced gas transfer in the presence of rain.However, the turbulent dissipation was measured at a fixed-point 30 cm from the surface aqueous boundary layer and thedynamics of the generation of the turbulence profile in thepresence of stratification were unclear. Measurements ofGreen and Houk [1979] and Lange et al. [2000] suggest thatturbulent mixing due to rainfall penetrates down toO(10)cm.Rain-induced density stratification may affect the turbulencein the surface aqueous boundary layer and the ability topredict k. Thus, the behavior and properties of these process-es need to be understood and measured for development ofadequate models for rain-induced gas exchange.[8] In the following, results of a follow-up experiment

conducted at the Biosphere 2 ocean, Bio2 RainX III, arepresented. The gas transfer velocity was determined byperforming an SF6 evasion experiment, as well as by imple-menting the active controlled flux technique (ACFT) [Zappaet al., 2004]. Raindrop size distributions and rain rates weremeasured with a Rain Imaging System (RIS) and a PassiveAcoustic Listener (PAL). Rain rates were also determinedwith a pressure transducer and with buckets. Turbulenceprofiles were measured with an acoustic DopBeam that alsomeasured the surface wavefield and rain rate. Records ofhigh-resolution temperature and salinity gradients were madeusing a profiling CTD (Seabird SBE-37), and the thermalsignature of water surface was measured using an infrared(IR) imager. Together, these measurements allow the studyof the influence of rain on air-sea gas exchange, as well asto elucidate the mechanisms responsible for the observedeffect.

2. Methods

[9] During Bio2 RainX III, four rain experiments wereconducted. The first (RE1) was a long rain event (175 min)with a moderate rain rate. The second (RE2) was a short rainevent (16 min) in an attempt to attain the maximum rain rateof the facility. The third (RE3) was another short event(24 min) at a moderate rain rate. The final (RE4) was a longrain event (134 min). The lengths of these rain events weredictated by the fresh water storage capacity of the reservoirs,by the range of tolerable water level in the Biosphere 2 ocean,as well as the salinity limit imposed by the requirements oforganisms in the ocean.

2.1. Biosphere 2 Ocean

[10] The Biosphere 2 ocean is ideally suited to conductcontrolled experiments on rain-induced air-sea gas exchangeand its utility has been well documented by Ho et al. [2004].The Biosphere 2 ocean contains 2,650 m3 of saltwater with anominal salinity of 35.5. The ocean has a surface area ofapproximately 675 m2 and much of the deep ocean is greater

C07009 ZAPPA ET AL.: RAIN-INDUCED TURBULENCE AND GAS TRANSFER

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than 6-m depth with a shelf reef that links the deep ocean atone end to a semi-enclosed lagoon at the other (see Figure 1).The ocean was maintained at a constant temperature of26.5�C by pumps that circulate the ocean water through aheat exchanger during all rain events except RE1. At the deep

end of the ocean, a vacuum wave generator along the entirelength of the wall creates energetic waves that propagatetoward the lagoon, circulate water in the ocean, and generateambient turbulence to promote air-water gas exchange. Fora more detailed description of the Biosphere 2 ocean, seeAtkinson et al. [1999] and Ho et al. [2004].[11] The rain generation system is supplied from two water

reservoirs (36 and 57 m3) using groundwater that had beenpurified by reverse osmosis. The system used for generatingrain during Bio2 RainX III consisted of a series of nine PVCpipes strung across the ocean. Descending from each pipewere 3 rain heads, for a total of 27 rain heads. The rain headswere commercially available irrigation devices modifiedwith short pieces of latex tubing that were oriented facingup (head inverted). Previous measurements show that theflexible tubing encouraged random dispersion of the drops,as well as a spectrum of drop sizes that was not too differentthan natural raindrop size distribution [Ho et al., 2004]. Therain heads were located 10 m above the ocean, allowingraindrops to approach terminal velocity before impacting thesurface. The nine lines of the rain generation system can beturned on and off independently depending on the desiredrain rate. Not using all 9 lines may result in spatial variabilityin the rain rate. During RE1, lines 1, 3, 5, 7, and 9 were used.During RE2, all 9 lines were used. During RE3 and RE4,lines 2, 4, 6, and 8 were used. Regardless of which lines wereused, the whole water surface including the ocean, the reefflat, and the lagoon, was agitated by rain.

2.2. SF6 Evasion Experiment

[12] An SF6 evasion experiment was conducted duringRE4 to obtain an integrated measurement of gas transfervelocity. The experimental methods and procedures werenearly identical to those used during Bio2 RainX II, anddescribed in detail by Ho et al. [2004]. About 12 h beforeRE4, a predetermined amount of SF6 dissolved in water(�1.3 � 10�5 moles) was injected into the ocean using a60 ml syringe. During RE4, samples for SF6 and salinitymeasurements were drawn from 14 different depths in theocean (1, 2, 3, 5, 8, 17, 34, 55, 75, 96, 141, 220, 410, and500 cm) every 20 min using a sample profiler [Ho et al.,2004]. Sampling for SF6 and salinity continued for 24 hafter RE4.[13] Water used to generate rain at Biosphere 2 during

RainX III contained a discernable amount of SF6 fromunknown sources. A correction was applied to the measuredSF6 concentration Cm(z) to deconvolve the decrease in SF6in the ocean due to gas exchange from the increase in SF6 dueto addition by rainwater and obtain a the corrected SF6concentration C(z):

C zð Þ ¼ Cm zð Þ s0

s zð Þ

� �� Cr

s0 � s zð Þs zð Þ

� �; ð2Þ

where s0 is the pre-rain ocean salinity, s(z) is the salinitymeasured concurrently with Cm(z), and Cr is the measuredSF6 concentration of the rainwater. The mean SF6 concentra-tion in the ocean and the gas transfer velocity were thendetermined using methods described by Ho et al. [2004](equations (2) to (6)).

Figure 1. The Biosphere 2 ocean: 45-m long, 19-m wide,with depth of the bottom varying from about 0.5 to 7 m.Indicated (as circled letters) are the locations of variousinstruments during Bio2 RainX III: a, SF6 and salinitysampler; b, pulse-to-pulse coherent Doppler sonar system(DopBeam) and Modular Acoustic Current System (MAVS);c, bottom-mounted YSI (temperature, pressure); d, autono-mous Seabird Microcat CTD Profiler; e, area measured byinfrared IR imager and used for active controlled flux tech-nique (ACFT); f, PAL; and g, Rain Imaging System (RIS).Also indicated are the 14 locations (numbered in squareboxes) for the 10-cm buckets in Table 2.


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[14] The gas transfer velocity for SF6 was normalized to aSchmidt number (Sc) of 600, corresponding to values forCO2 at 20�C using the relationship:

k 600ð Þ ¼ kSF6

600

ScSF6

� ��n

; ð3Þ

where kSF6and ScSF6

are the gas transfer velocity and theSchmidt number for SF6 (828 for our experiment),respectively. It has been shown in models and experimentsthat for a clean wavy water surface, in the absence of bubbles,n equals 1/2 [Brumley and Jirka, 1988; Jahne et al., 1987;Ledwell, 1984].

2.3. Rain Rate and Drop Size Distribution

[15] The raindrop size distribution (DSD) was obtainedusing the Rain Imaging System (RIS) developed at NASAand described in detail by Ho et al. [2004]. The RIS is anoptical system consisting of an analog black and white videocamera that is pointed at a halogen flood lamp. The RIScamera and light were located on the coral reef (see Figure 1).[16] Ho et al. [1997] proposed and subsequent studies have

shown [Ho et al., 2000, 2004] that rain-induced air-water gasexchange is correlated to rain kinetic energy flux (KEF).Recently, Takagaki and Komori [2007] proposed that themomentum flux of the raindrops (MF) is the more relevantscaling parameter. The KEF and MF are defined as

KEF ¼ 1

2rVv2nd ¼

1

2rRv2 ð4aÞ

MF ¼ rVvnd ¼ rRv ð4bÞ

where r is the density of water, V is the volume of a raindrop,R is the rain rate, nd is the number of raindrops, and v is thevelocity of the raindrop in cm s�1.[17] Takagaki and Komori [2007] suggest that their gas

transfer velocities were well parameterized by MF, but notwith KEF. However, their data show only slightly betteragreement with an MF scaling at low MF and KEF but alsoshow slightly better agreement with a KEF scaling at higherMF and KEF. Their results actually show no statisticallysignificant difference between a correlation of k with MF orKEF. Furthermore, comparisons with the previous rain andgas exchange studies show that both KEF and MF collapsethe data similarly and no difference can be concluded. Thissuggests that KEF is nearly equivalent to MF for theparameterization of rain-induced gas transfer.[18] Our current data set will not provide a conclusive

answer to the KEF or MF debate. However, the raindrop sizedistributions and raindrop terminal velocities described hereare comparable to those found in nature. The purpose of ourstudy is to explore the effect of turbulence (TKE dissipationrate) and stratification on the rain-induced gas exchangeincluding the implementation of a turbulence closure modelthat is intrinsically based on energy arguments. Therefore, wehave chosen to present KEF for the purpose of our presentwork and for consistency with our previous studies.

[19] KEF can be derived from a DSD according to:

KEF ¼ r2

p610�6

Zv3D3NdD ð5Þ

where N is the raindrop size distribution, D is drop diameterin cm, v is the velocity of the raindrop in cm s�1, and KEFhas units J m�2 s�1. At Biosphere 2, the 10 m height wassufficient for drops to approach terminal velocity. Thus,a relationship of Lhermitte [1988] was used as a realisticestimate of drop terminal velocities v in the RISmeasurementvolume:

v Dð Þ ¼ vo 1� exp � 6:8D2 þ 4:88D� ��

ð6Þ

where vo is 923 cm s�1 assuming that the measurement isperformed at ground level.[20] We also deployed a Passive Aquatic Listener (PAL) to

quantify rain rate and drop size distribution during Bio2RainX III. The PAL consists of an ITC-8263 hydrophone,signal pre-amplifiers and a recording computer (Tattletale-8).Details on the instrument description and application aregiven by Ma and Nystuen [2005]. The nominal sensitivityof these instruments is �160 dB relative to 1 V mPa�1 andthe equivalent oceanic background noise level of the pre-amplifier system is about 28 dB relative to 1 mPa2 Hz�1. Adata collection sequence consists of four 1024 point timeseries collected at 100 kHz (10.24ms each) separated by 5 s iftriggered by rain or drizzle. Each time series is fast Fouriertransformed (FFT) to obtain a 512-point (0–50 kHz) powerspectrum. These four spectra are averaged together andspectrally compressed to 64 frequency bins, with frequencyresolution of 200 Hz from 100 to 3,000 Hz and 1 kHz from3 to 50 kHz. These spectra are evaluated individually todetect the acoustic signature of rainfall and then are recordedinternally. The drop size distribution is then calculated by anacoustic inversion technique described by Nystuen [2001].[21] The spatial distribution of the simulated rain was

assessed using water volume measurements from twelve10-cm diameter buckets. The buckets sat on floats, whichwere each tethered by a 1-m line to one of two ropes thatextended from the wave generator to the beach. A YSIpressure and temperature sensor was deployed on the bottomof the deep part of the ocean (see Figure 1). The pressuresensor was used to estimate the bulk rain rate for the wholereservoir by taking the increase in depth over time.

2.4. High-Resolution Temperature and Salinity Profiles

[22] The evolution of a freshwater lens both during andafter the rain events was important to quantify during Bio2RainX III. High-resolution vertical profiles of salinity andtemperature were measured using a Seabird Microcat ModelSBE 37-SIP raised and lowered on an automated pulleysystem. The pulley was suspended from the ceiling abovethe ocean and a DC motorized winch was used to controlthe sensor depth in the water. During the experiment, theMicrocat was deployed at the deep end of the ocean (6.5 m),adjacent to the wave generator (Figure 1). To minimize wakecontamination from instrument and wire perturbation, onlythe upward profiles were used since the instrument sensorswere facing upward. The Seabird Microcat sensor was setto report data at 1-s intervals, and was raised and lowered at


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4.81 cm s�1. Data output from the sensor was used to regulatethe vertical excursion of the sensor by stopping the motionwhen the detector reached the water surface on the upwardmotion and 4.5-m depth on the downward motion. Profilesweremade every 3min, starting at depth, rising to the surface,pausing, and then returning to depth.

2.5. Turbulence and Wave Measurements

[23] Measurements of velocity were made using a coherentDoppler sonar. The DopBeam (Sontek) is a 1.5-MHz mono-static, single-beam sonar system performing pulse-to-pulsecoherent Doppler measurements of the along-beam fluidvelocity. Details on the DopBeam operation and implemen-tation are given by Zedel et al. [1996] and Veron and Melville[1999]. For our configuration, the DopBeam measuredvelocities at a repetition rate of 375 Hz along the beam in125 bins 1.2 cm width each. During the pulse-pair process-ing, the velocity is determined by taking the time rate ofchange of the phase of the complex signal autocorrelation andis averaged down to 10 Hz. A ‘‘dead’’ zone exists within15 cm of the 2.5-cm diameter transducer where the DopBeamis not able to measure velocity because of the delay betweentransmitting and receiving the acoustic signal. The cutoff forthe correlation coefficient is given as 0.85 below which isdefined as bad data from the DopBeam.[24] A second velocity measurement was provided by a

modular acoustic velocity sensor (MAVS; Nobska) by mea-suring the differential travel time of an acoustic pulsebetween a transmitter and receiver. The MAVS provided ameasurement of x, y, and z axis velocity components (u, v,and w, respectively). Mean flow velocity and turbulentvelocity (dissipation rate) statistics were estimated from10 min records sampled at 22 Hz. The mean current iscalculated as V = (�u2 + �v2)1/2 where overbars denote 10 minaverages.[25] The DopBeam was rigidly boomed out horizontally

from the dock such that the acoustic transducer/receiver headof the instrument was 3 m from the dock at an initial depth of0.7 m and directed toward the ocean surface (see Figure 1).The MAVS Instrument was mounted similarly such that thesensing volume was at a depth of 0.5 m and 0.75 m adjacentto the DopBeam. The locations of the DopBeam and MAVSduring Bio2 RainX III are shown in Figure 1. In thisconfiguration, the DopBeam provides a profile of verticalvelocity near the ocean surface and the MAVS providescontinuous 3-component velocity at depth.[26] In steady flow with isotropic, fully developed turbu-

lence, kinetic energy is transferred from the mean flow tolarge eddies, then on to smaller eddies, and is finallydissipated by viscosity. Under these conditions, the turbulentdissipation rate, e, can be estimated by the magnitude of thewave number spectrum in the inertial subrange. The inertialdissipation method is used to determine e from

S ¼ A18

55e2=3k�5=3 ð7Þ

where S is the one-dimensional wave number spectrum of theturbulent velocity, k = 2pf/V is the wave number, V is themean current, f is the frequency, and A is taken to be 1.5.[27] Measurements of the turbulent dissipation rate, e,

were made in the Biosphere 2 ocean according to the model

for the inertial subrange of the kinetic energy spectrum in (7)using bothMAVS and the DopBeam. Assuming an extensionof Taylor’s hypothesis of frozen turbulence (e.g., steadycurrent) for unsteady advection (e.g., waves) [Lumley andTerray, 1983], the measured frequency spectra of verticalvelocity were converted to wave number space by k = 2pf/Vand e is calculated from (7). A safe lower bound of the iner-tial range is determined according to the criterion kz > 5.A reasonable upper bound is determined according to thecriterion kL < 1, where L is the length scale of the samplevolume. Before calculating the dissipation rate, the depth-averaged velocity is removed from each bin of the DopBeamto effectively remove the velocity signal due to the waves.In this mode of calculation, the DopBeam gives a profile ofdissipation rate up to just beneath the surface while theMAVS gives an estimate of e at a fixed depth of 50 cm.TheDopBeam can also be used tomeasure e directly from thewave number spectrum in (7) [Veron and Melville, 1999]without the need for Taylor’s hypothesis. Comparison ofthese two distinct estimates in space-time chunks of 20 cmover 10 min show that the difference between the twoestimates is within 10% for dissipation rates ranging from10�6 to 10�2 W kg�1.[28] The DopBeam also characterized the wavefield that

existed during Bio2 RainX III by using the high signal returnof the water surface as an estimate of the surface waveelevation. It measured the instantaneous surface elevationto within ±1.2 cm at a sample frequency of 20 Hz. Measure-ments were made continuously whenever the DopBeam wasoperational. Significant wave height was calculated from theRMS of the surface elevation and the dominant wavefrequency was determined as the peak in the power spectraof surface elevation. The high signal return of the watersurface was also used to estimate the bulk rain rate for thewhole reservoir by taking the increase in distance to the watersurface over time. The nominal value throughout all rainevents was a significant wave height Hs of 2.45 cm and apeak frequency fp of 0.21 Hz.

2.6. Active Controlled Flux Technique

[29] Analogous to gases that move through the surfaceboundary layer by diffusion, a net heat flux occurs throughthe aqueous thermal boundary layer (TBL) by molecularconduction at the surface [Katsaros, 1980; Robinson et al.,1984]. Because of evaporation, the temperature at the watersurface, or skin, is typically less than the bulk temperatureimmediately below by several tenths of a degree Celsius[Donlon and Robinson, 1997; Schlussel et al., 1990; Wicket al., 1996].[30] By measuring the fine-scale horizontal structure in

skin temperature, passive infrared (IR) imagery is used toexplore the impact of turbulence at water surfaces within theTBL. The thickness of the aqueous thermal boundary layer isof O(10�2–10�3)m [Hill, 1972; McAlister and McLeish,1969; Wu, 1971]. However, the optical depth of the infra-red radiation detected, on average 35 mm for the spectralwavelength band of 3–5 mm [Downing and Williams, 1975;McAlister and McLeish, 1970], is much less than the TBLthickness. Therefore, an IR imager is ideally suited to mea-sure the skin temperature and turbulent disruptions of theTBL. Large-scale wave breaking [Jessup et al., 1997],microbreaking [Zappa et al., 2001, 2004], near-surface shear,


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and free-convective patchiness [Zappa et al., 1998] are allturbulent processes that produce signatures of thermal vari-ability quantified by IR imaging techniques. Likewise, tur-bulence generated by rain impinging on the air-waterinterface dominates the disruption of the TBL by an enhance-ment of surface renewal [Craeye and Schlussel, 1998;Schlussel et al., 1997]. Thus, IR measurements of the TBLprovide the means to remotely examine turbulence interact-ing with the free surface.[31] An IR imaging system was used to visualize the

turbulence within the TBL generated by the rain and toimplement the ACFT. The infrared measurements were madeusing an Amber model Radiance HS infrared imager (AmberEngineering, Goleta, CA) that responds to radiation in thespectral band of 3–5 mm. It was mounted 9.5 m above theocean at an incidence angle of roughly 20� to the surface.This configuration resulted in roughly a 2 � 2 m image sizewith smaller than 1-cm resolution, and the IR imagery wasdigitized at a frequency of 30 Hz. A nonuniformity correctionand a calibration were performed before each run during theexperiment using a Santa Barbara Infrared model 2004Sblackbody (SBIR, Santa Barbara, California). The noiseequivalent temperature difference (or mean resolvable tem-perature difference) was determined to be ±0.02�C using theisothermal blackbody calibration target.[32] The active controlled flux technique (ACFT) relies on

heat as a proxy tracer for gas according to unsteady diffusioncombined with surface renewal theory to estimate k [Asheret al., 2004;Atmane et al., 2004; Zappa et al., 2004].With theACFT, the water surface is heated with a CO2 laser to producea spot with a measurable temperature difference that can be

tracked within a sequence of infrared images. A Synradmodel G48-2-28(W) continuous-wave 25-W CO2 laser op-erating at 10.6 mm was directed at the water surface fromabove the Biosphere 2 ocean using a series of 5-cm diameterIR mirrors, and was pulsed for 10 ms with a gating frequencyof roughly 0.25 Hz. The laser beam generated heated spots onthe water surface in the field of view of the infrared imagerroughly 7–8 cm in diameter. For the runs used to determinethe decay time from the CFT, the infrared imagery wasdigitized at a frequency of 30 Hz.[33] The transfer velocity of heat, kH, is determined from

the surface renewal rate, l, which is estimated from thethermal decay of the heated spot as predicted from a surfacerenewal model. The method employed by Haußecker et al.[1995] fits the normalized surface temperature, TN, of thepatches tracked by the ACFT to

TN ¼ hffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ 4at

p e�lt ð8Þ

where h is the penetration depth and a is the thermaldiffusivity of water. The heat transfer velocity is calculateddirectly from l using

kH ¼ffiffiffiffiffiffial

pð9Þ

where the functional form of (9) is specific to a surfacerenewal model where the probability distribution of thesurface element lifetimes is defined by an exponential dis-tribution [Danckwerts, 1951]. Jahne et al. [1989] have assertedthat the gas transfer velocity, k, should scale directly to thetransfer velocity of heat by

k ¼ kHSc

Pr

� ��n

¼ kH Leð Þ�n ð10Þ

where Pr is the Prandtl number of heat, and Le is the Lewisnumber. According to the scaling predicted by (10), previousACFT laboratory measurements yield values of kH that,when scaled to a common value of Sc, agree with kmeasuredusing conventional gaseous tracers [Haußecker et al., 1995;Jahne et al., 1989]. A limitation of the technique may be thatnot all eddies that affect the MBL and renew the surface arecomplete and instantaneous. More recent field and laboratorystudies have led to improvements in the technique [Asheret al., 2004; Atmane et al., 2004; Zappa et al., 2003, 2004]and to the suggestion of modeling k using penetration theory[Harriott, 1962] rather than surface renewal when imple-menting ACFT. The choice of n is difficult to determine innatural systems when using this technique. ACFT ideallyshould be complemented with a tracer technique [Clark et al.,1994], as has been done here, or another suitable method fordetermining the gas transfer.

3. Results

3.1. Rain Rate and Drop Size Distribution

[34] During Bio2 RainX III, RIS, measured DSDs for RE1,RE2, and RE4, respectively. The DSD for RE4 is derivedfrom more than 50,000 drops, and is shown in Figure 2.As commonly observed in natural rain, the DSD reveals that

Figure 2. Raindrop size distribution (DSD) measured byRIS and PAL during RE4, as well as the Marshall-PalmerDSD. Relative to natural rain, the simulated rain at Biosphere2 during RainX III tends to be enhanced for small drops(0.75–1.5 mm) and larger drops (3.0–4.0 mm) but deficientfor moderate drops (between 1.5 and 3.0 mm) according tothe RIS. DSD by RIS from RainX II is also shown forcomparison. RainX II DSD shows consistently more drops ofevery diameter except between 1 and 2 mm where the DSDare roughly the same.


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the drop density decreases with increasing drop size. Thedrop size range measured by the RIS and therefore used tocompute rain rates and KEFs was from 0.3 to 5.3 mm diam-eter. The DSD according to the Marshall-Palmer (M-P)distribution [Marshall and Palmer, 1948] is also shown inFigure 2. This allows for the comparison of the simulated rainto natural conditions. The M-P distribution is given by

N Dð Þ ¼ N0 Rð Þ exp �LDð Þ ð11Þ

where N0 = 8� 104 m�3 cm�1 and L = 42.3� R�0.214 cm�1

from Olsen et al. [1978] are used because R between modelinput and output is conserved. The DSD measured duringRE4 by RIS shown in Figure 2 closely resembles the M-PDSD. However, some small differences highlight the vari-ability in the simulated DSD. The simulated rain tends to bedeficient in drops smaller than 0.75 mm and in the size rangeof 1.5–3 mm, and tends to be enhanced for drops in thesize range of 1–1.5 mm and 3–4 mm. DSD by RIS fromRainX II is also shown for comparison. RainX II DSD showsconsistently more drops of every diameter except between 1and 2 mm where the DSD are roughly the same. Analysisof the RIS DSDs indicates that using the M-P DSD insteadof measured DSDs would only underestimate the KEF by4.1%.[35] The DSD from PAL inversion in Figure 2 is shown

to underestimate the RIS DSD for 1.0 mm drops and over-estimates the RIS DSD for 4.5 mm drops. The PAL inversionis based on four raindrop categories of special acousticsignatures. These few large bin sizes similarly can lead todeviation from the Marshall-Palmer distribution and theestimated rain rate. Note also that the inversion matrix forPAL was developed empirically according to field data in afreshwater pond in Florida. The study at Biosphere 2 was thefirst attempt to invert the DSD from laboratory PAL data ina saltwater environment. PAL provides a circular footprintof the surface whose radius is roughly 3 times the depth.For Biosphere 2, PALwas at a depth of 6.5 m and its footprintwas �20 m. Also, the geometry of the confined Biosphere 2ocean can produce resonant sound (increased sound level)which could affect the accuracy of DSD inversion and itsrelation to the Marshall-Palmer distribution as well as therain rate.[36] All the estimated rain rates are summarized in Table 1.

Rain rates determined from the YSI pressure probe, theDopBeam, the buckets, the PAL Inversion, the PAL Singlef, and RIS. The YSI and DopBeam estimates of the rain rateare intrinsically a basin-wide mean estimate and on averageare within 12% of each other for all experiments. RE1 andRE4 show the closest agreement between the YSI andDopBeam since the duration of these experiments allowedfor significant accumulation in the ocean basin. The bucketsprovide multiple local estimates scattered throughout the

basin while the RIS provide single point measurements ofthe rain rate. These local estimates are summarized in Table 2and suggest considerable spatial variability. Additionally, thestandard deviation among the buckets for a given rain eventranges from 17.2% to 32.1%. The observed variability in rainrate over the ocean basin is likely due to irregularities in therain generation system itself as discussed byHo et al. [2004].[37] Although the bucket, PAL, and RIS data provided

estimates of the average rain rates, the considerable spatialvariability heterogeneity called for a more consistent methodto derive average rain rates. Therefore, theYSI andDopBeamhave been used to provide the baseline basin-averaged rainrates. The DSD measured by RIS is assumed to hold overthe entire ocean and scaled by the average rain rate, so thespatially averaged global ocean KEFs were 0.19 ± 0.02 J m�2

s�1 and 0.31 ± 0.02 J m�2 s�1 for RE4 and RE1, respectively.Likewise, local rain rates are used to scale these global KEFsto local transfer velocities and dissipation rates later in theResults and Discussion.

3.2. Gas Transfer Velocity

[38] The observed SF6 concentration in the Biosphere 2ocean decreases rapidly with the onset of rain. Contrary toBio2 RainX II [Ho et al., 2004], where part of the effect is dueto dilution of SF6 tagged oceanwater with SF6-free rainwater,during Bio2 RainX III, rainwater actually added SF6 to theocean. The dilution corrected data is shown in Figure 3. Withthe onset of rain, SF6 is quickly lost from the surface layer(<100 cm) because of enhanced air-sea gas exchange. Thecombined effect of the wave generator, circulation pumps,and rain caused the k(600) to be 34.9 ± 6.2 cm h�1 for RE4.The k(600) for no rain conditions in previous experiments atBiosphere2 duringRainEx IIwas 11.2 ± 0.3 cmh�1 [Ho et al.,2004].

Table 1. Summary of Rain Rate Conditions During Bio2 RainX IIIa

Rain Event YSI DopBeam Buckets PAL Inversion PAL Single f RIS

1 39.5 43.0 49.5 30.9 44.4 77.02 47.7 60.3 75.0 43.4 52.4 80.13 24.3 28.8 35.3 32.9 48.4 N/A4 30.8 31.9 38.2 33.3 46.9 28.7

aAll units are in mm h�1.

Table 2. Individual Rain Rate Conditions as Measured by the

10-cm Buckets During Bio2 RainX IIIa

Location RE1 RE2 RE3 RE4

1 60.2 79.2 32.2 19.42 59.8 96.8 53.4 36.33 38.1 57.2 27.6 28.34 51.7 70.4 35.0 36.65 48.2 – 29.4 33.36 48.2 – 33.1 54.97 33.4 30.8 18.4 33.88 53.6 – 19.3 20.59 52.4 105.6 51.5 59.910 54.4 88.0 43.3 44.111 35.3 – 35.9 40.512 47.0 70.4 38.7 –13 57.1 90.2 48.8 52.414 53.6 61.6 27.6 36.6aAll units are in mm h�1. For cases when the buckets tipped over during

the rain event, no data were recorded. The RIS is nearest to location 5. TheDopBeam is nearest to location 11.


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3.3. High-Resolution Air-Water Transfer Ratesand Near-Surface Turbulence

[39] The SF6 tracer gives a temporally averaged basin-wide gas transfer velocity. Measurements of the transfervelocity by ACFT allow one to examine the temporalbehavior of the processes driving the exchange. The magni-tude of k measured by ACFT was comparable for all fourrain events during Bio2 RainX III. Figure 4a shows a timeseries of the transfer velocity, kH(600) determined by ACFTreferenced to Sc = 600 spanning before, during and followingRE1. Both 30 s and 5 min averages for kH(600) are given inFigure 4a. Before RE1 begins, kH(600) is 13.5 cm h�1. Assoon as the rain begins, kH(600) rises quickly to 27 cm h�1

and plateaus around 33–34 cm h�1. As the rain continues,kH(600) begins to drift down to an equilibrium level around30 cm h�1. At the completion of RE1, kH(600) returns toits pre-RE1 level of 12 cm h�1.[40] Measurements of kH(600) for RE4 are shown in

Figure 5a and exhibit similar characteristics to RE1. kH(600)

abruptly increases at the onset of the rain event from the non-rain value of 12.7 cm h�1. In the early stages of RE4, kH(600)varies between 24 and 26 cm h�1, and as the rain continueskH(600) increases slightly and stabilizes at 27 cm h�1. At theend of RE4, kH(600) returns to its pre-RE4 level.[41] Near-surface turbulence is thought to be responsible

for air-sea gas transfer, and k has been modeled and shown toscale with e1/4 [Lamont and Scott, 1970]. Figure 4b shows thetemporal evolution in turbulence dissipation rate as a func-tion of depth at the beginning, during, and end of RE1 in theBiosphere 2 ocean. The calculation of e is described above.Prior to the beginning of RE1, background e levels measuredat roughly 50 cm depth with the MAVS were 5� 10�6 to 1�10�5 W kg�1. As the rain begins, the surface value of eincreases abruptly by several orders of magnitude to 1.0 �10�2 W kg�1. The turbulent dissipation rate decays signifi-cantly with depth to levels of 3.0� 10�5W kg�1 at a depth of25 cm. Surface values of e remain above 1.0� 10�3 W kg�1

for nearly an hour. Following the peak plateau, e decreases to

Figure 3. Depth measurements of SF6 concentration as a function of time during RE4. The inset is anenlargement of the top 100 cm of the ocean during the rain event. Each black dot denotes a sample. SF6concentration has been corrected for dilution according to equation (2).


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an equilibrium level of 3 � 10�4 W kg�1 until the rainterminates. The variability of e at this single location issignificant.[42] Measurements of e during RE4 are shown in

Figure 5b. Note that the circulation pumps are running duringRE4 that adds to the background turbulence. As a result, theturbulent dissipation rate throughout the bulk fluid staysnearly constant at 3.0 � 10�5 W kg�1. As the rain begins,the turbulence at the surface increases above backgroundlevels to roughly 3.0 � 10�4 W kg�1. Surface values of eincrease to an equilibrium level of 2� 10�3 W kg�1 until therain terminates. Both kH(600) and e track each other very welland suggests a causal relationship between the turbulencegenerated by rain impinging at an air-water interface and theair-water gas exchange rate.

3.4. High-Resolution Temperature and Salinity Profiles

[43] Figure 6 shows the temporal evolution in oceantemperature, salinity, density and the Brunt-Vaisala fre-quency squared, N2, as a function of depth at the beginning,during and end of RE1 in the Biosphere 2 ocean. The cal-culation of N2 is determined from (g/ro)(dr/dz) where g isthe acceleration due to gravity, ro is the reference density,and dr/dz is the density gradient.

[44] Before the start of RE1, the density was homogeneousthroughout the water column on the basis of previousobservations (not shown) [see Ho et al., 2004]. The presenceof the rain had a delayed effect on the surface layer, where afresh, warm lens developed after just under an hour into therain event. Localized, instantaneous stratification is likely tohave been present early during RE1, but it was not measur-able. During RE1, the salinity dropped from an initial valueof 35.7 to a minimum of 32.5; the initial temperature was25.6�C, and reached a maximum of 25.78�C at the surface.The density is clearly driven by the salinity and drops from aninitial value of 1023.7 kg m�3 to a minimum surface value of1021.1 kg m�3. Most noticeable is the stratification asmeasured byN2 showed a distinct gradual deepening roughlyan hour into the rain event to a depth of 20 cm. This stratifiedlayer with N2 values greater than 0.03 rad2 s�2 lasted for theduration of the rain event. At the completion of the rain event,this stratification level disintegrates while a layer at 1.5 mdepth that had developed previous to the end of the rain eventstrengthens. After the rain ceased, the fresher surface layercontinued to mix down into the ocean interior to an asymp-totic depth of 3.5 m. Even after 2 full days, the ocean had notre-established its pre-rain state because the pumps had beenturned off during this rain event.[45] Subsequently, RE4 (Figure 7) showed similar behav-

ior to that during the RE1. Here, a fresh, cold lens developedduring the rain event. During RE4, the salinity droppedfrom an initial value of 34.7 to a minimum of 32.8; theinitial temperature was 25.37�C, and reached a minimumof 25.26�C at the surface. The density again is clearlydriven by the salinity and drops from an initial value of

Figure 4. (a) Time series of the transfer velocity kH(600)determined by ACFT referenced to a Schmidt number of 600spanning before, during, and following RE1. The red dots are30-s averages, and the large blue dots are 5-min averages.(b) Temporal evolution of turbulence dissipation rate e as afunction of depth at the beginning, during, and end of RE1in the Biosphere 2 ocean.

Figure 5. Same as Figure 4 for RE4.


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1023.2 kg m�3 to a minimum surface value of 1021.6 kg m�3.Most noticeable is that the stratification is significantlyless than observed during RE1. The stratified layer withN 2 values between 0.02 and 0.03 rad2 s�2 becomesevident more than halfway through the rain event and nosecondary deeper layer is apparent. This is likely due tothe enhanced mixing caused by the circulation pumps.After the rain ceased, the fresher surface layer continued tomix down into the ocean interior to an asymptotic depth of2.0 m. and the ocean became well-mixed within a day.

4. Discussion

4.1. Comparison of RainX Gas Transfer Velocitiesto KEF Relationship

[46] The bulk tracer results presented here confirm theprevious finding byHo et al. [2004] that rainfall on the oceanenhances the air-sea gas exchange rate. k(600) was 34.9 ±6.2 cm h�1 during RE4 with energy input from the wavegenerator, the circulation pumps, and from rain. The k(600)for no rain conditions in previous experiments at Biosphere 2during RainX II was 11.2 ± 0.3 cm h�1 [Ho et al., 2004], sothe difference in k(600) between the rain and no rain con-ditions is 23.7 cm h�1 at a KEF of 0.19 J m�2 s�1. Note thatk(600) for the RE2 during RainX II was reported incorrectlyby Ho et al. [2004] and is in fact 44.6 ± 5.4 cm h�1, so the

difference in k(600) between rain and no rain conditionsduring RainX II was 33.4 cm h�1 at a KEF of 0.37 J m�2 s�1.Both the value reported here from RainX III and the updatedvalue fromRainX II fall within the bulk relationship shown inFigure 8 between k(600) and KEF established by Ho et al.[2000].[47] It is likely that bubble-mediated exchange plays a role

in the Biosphere 2 saltwater ocean as it did in the freshwatermeasurements byHo et al. [2000] and will be discussed later.Mean transfer rates from the ACFT for all rain events and onenon-rain event are shown in Figure 9a and range between12.9 and 31.7 cm h�1. We note a reasonable correlation ofkH(600) with increasing rain rate (coefficient of determina-tion of 0.987) for the range of values investigated. The SF6evasion and ACFT results showing an increase in transfervelocity due to rain is consistent with the physical measure-ments of turbulence and stratification made during RE1 andis described in detail in the following section.

4.2. Relationship Between High-ResolutionTurbulence, Stratification, and Transfer Velocity

[48] The high-resolution transfer rate and turbulenceresults presented here clearly show the causal relationshipbetween rainfall and air-sea gas exchange. Rainfall imping-ing on the ocean surface enhances the turbulent dissipationrate, which in turn controls the rate of air-sea gas transfer.Turbulent kinetic energy is generated during the rain eventswith the impact of each raindrop on the water surface and isFigure 6. Time series plot of the temperature T, salinity S,

density r, and the Brunt-Vaisala frequency squared, N2, fromthe autonomous profiling MicroCat for RE1 over the upper2 m of the Biosphere 2 ocean. The calculation of N2 isdetermined from (g/ro) (dr/dz), where g is the accelerationdue to gravity, ro is the reference density, and dr/dz is thedensity gradient.

Figure 7. Same as Figure 6 for RE4. Note that the colorscale for temperature has a range of 0.15�C as in Figure 6 andthat the scales for salinity, density, and N2 are identical asthose presented in Figure 6.


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delivered to the surface layer of the ocean. The cumulativeresult caused an increase in e (Figures 4b and 5b) andkH(600) (Figures 4a and 5a). IR imagery shows that raindropsimpacting the water surface generate disturbances of thesurface aqueous boundary layer with the horizontal scalesof energetic mixing at the surface of O(10 cm) that arecomparable to the vertical scales of mixing during the rainevents and observed in previous laboratory studies [Greenand Houk, 1979; Lange et al., 2000]. Following this increasein e and enhanced transfer rate, stable stratification developed(Figures 6 and 7; increase in N2) because of the addition offreshwater by rain and suppresses turbulent mixing near thesurface, causing e to decrease slightly. This stratified inter-face deepens to roughly 20 cm and effectively traps theenhanced turbulence in the near-surface layer. This forces eand kH(600) to remain constant, yet significantly enhanced,for the duration of the rain event. At the conclusion of the rainevent, the stratified interface at 20-cm depth disintegratesrapidly, e diminishes to pre-rain event levels, and the transferrate plummets to the no-rain condition. This stratification thatleads to the trapping of e near the surface will not only have aprofound effect on the enhanced kH(600), but also will play arole in diminishing the vertical mixing of mass transported tothe air-water interface that is important as the driving poten-tial in the flux of gas.[49] The secondary stratified interface that develops at a

depth of 1.25 m during RE1 as observed in Figure 6 suggeststhat the erosion of the stratified layer has begun even whilethe near-surface stratified interface at 20-cm depth persistsuntil the rain event has concluded because of the constantsupply of freshwater to the layer. This suggests a balance ofthe KEF input with dissipation in the near-surface layer above

the stratified layer, damping of turbulence by the stratifica-tion, and diffusion of turbulent energy via entrainmentdeepening of the stratified layers. The balance assumes aminimal horizontal advection of energy. The turbulence dueto the raindrops significantly enhances mixing. These obser-vations are an interesting first glimpse of an overlappingtransition from the rain-driven quasi steady state stratifiedlayer to deepening of this layer by entrainment that initiates ata significantly deeper layer.[50] During RE4, the circulation pumps were operating

and caused significant background turbulence as evidencedby comparison of Figures 4b and 5b. In addition, the warmfresh lens of RE1 produces a statically stable system, whilethe cold fresh lens of RE4 generates a diffusively unstablesystem. The diffusively unstable system resulted in slightly

Figure 8. Gas transfer velocity versus kinetic energy fluxKEF. Freshwater data represent distinct raindrop sizes withdiameters of 2.3 mm, 2.8 mm, and 4.2 mm from experimentsat the Wallops rain facility and are summarized by Ho et al.[2000]. Saltwater data represent broad raindrop size distri-butions and are from RainX II [see Ho et al., 2004] and thisstudy of RainX III at Biosphere 2.

Figure 9. (a) The transfer velocity kH(600) determined byACFT referenced to a Schmidt number of 600 and (b) turbu-lent dissipation rate e both as a function of rain rate.


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enhanced surface turbulence over the statically stable systemas evidenced by the higher surface values of e and the weakerstratification via N 2. The higher bulk levels of e and weakerstratification result in a speeding up of the entrainmentprocesses described above that potentially hinder the devel-opment of the secondary stratified layer.

4.3. Comparison of Dissipation Rates During RainXExperiments to Breaking Wave Measurements

[51] During Bio2 RainX III, near-surface e ranged from10�6 W kg�1 in the absence of rain to instantaneous levels of10�2 W kg�1 during RE1 as shown in Figures 4b and 5b, andobserved for the other rain events. These levels during rainevents are O(100) W kg�1 greater than observed duringRainX II because the measurements during RainX III weremade at the surface compared to the bulk measurements ofRainX II. Sustained mean dissipation rates for all rain eventsare shown in Figure 9b and range between 2.7 � 10�4 and4.9 � 10�4 W kg�1. The mean dissipation rates in Figure 9bwere calculated as the average of the top 2 bins during anindividual rain experiment. No distinct relationship wasfound for dissipation rate as a function of rain rate for thenarrow band of values investigated. For comparison, esti-mates of e beneath breaking waves ranged from 10�5 to10�2 W kg�1 on the open ocean [Gemmrich and Farmer,2004] and on lakes [Agrawal et al., 1992; Terray et al., 1996].The results demonstrate that rain forcing significantly enhan-ces turbulence under no wind conditions in the Biosphere 2ocean and that near-surface e is comparable tomoderate wavebreaking. Instantaneous dissipation rates during strong rainevents were found to be similar to those found beneath strongbreaking waves. Raindrops are ubiquitous, and the uniformsurface mixing and subsequent air-water gas exchange arecomparable to other dominant processes such as wavebreaking.

4.4. Effects of Bubble-Mediated Exchange on RainXResults

[52] Bubble-mediated exchange is an important conduitfor air-sea gas transfer [Asher et al., 1996; Keeling, 1993;Woolf and Thorpe, 1991; Woolf, 1993] and is intrinsic to thecomparisons between measurements from RainX experi-ments in the Biosphere 2 saltwater ocean and the experimentsperformed in freshwater at the Rain-Sea Interaction Facility(RSIF) shown in Figure 8. The bulk KEF relationship of Hoet al. [1997] was developed using the freshwater measure-ments that included the presence of bubbles at RSIF. Thebubble generation characteristics are different in salt waterand freshwater systems. Bubble-mediated gas transfer isinfluenced by the size of the bubbles, the penetration depthsof the bubbles, the rise velocity of bubbles, the solubilityof the gas, the diffusivity of the gas, and the presence ofsurfactants. Raindrops generate large bubbles at the surfacethat remain near the surface without penetrating to deeperthan O(10 cm) [Ho et al., 2000]. Each bubble of a particulardiameter has an equilibrium depth at which its rise to thesurface corresponds to the time it takes for a specific gas toequilibrate completely with the bubble volume and thereforemaximize its bubble-mediated gas transfer. Therefore, manysmall bubbles have an equivalent impact on the transfervelocity as does a significantly fewer number of large

bubbles. Typically, rain on freshwater shows bubble sizedistributions with many large bubbles but fewer total bub-bles, as observed in the data ofHo et al. [2000], since bubblesare more likely to coalesce in freshwater but less so insaltwater [Asher et al., 1997; Scott, 1975]. (Note that largebubbles generated during rain events may not be in closeenough proximity to coalesce.) Therefore, it is important tonote the difference between the rain data from the freshwaterat RSIF and the saltwater ocean in Biosphere 2.[53] The raindrops in RSIF were distinct sizes of 2.3, 2.8,

and 4.2 mm while the raindrops produced in the RainX IIand RainX III had broad distributions as shown in Figure 2.Here, there were significantly more smaller drops because ofthe broad DSD as opposed to the discrete raindrops of 2.3,2.8, and 4.2 mm by Ho et al. [2000]. The total number ofraindrops calculated in each experiment shows that duringRainX II and III there were at least 20 times as manyraindrops relative to the RSIF experiments at the sameKEF. Furthermore, the RSIF data show that for a givenrain rate there are significantly more bubbles generated bythe 2.8-mm drops than the 4.2-mm ones because the totalnumber of bubbles generated is correlated with the totalnumber of raindrops hitting the water surface. Assuming thislinear relationship between the number of raindrops and thenumber of bubbles, the rain data from the two RainX experi-ments in Biosphere 2 would be expected to give a higher gastransfer rate compared to the RSIF data because of enhancedbubble-mediated exchange strictly by the difference in DSD.In Figure 8, however, the Biosphere 2 measurements fallwithin the bands of the RSIF results. An expected increasedbubble-mediated component in Biosphere 2 is compensatedby a decreased contribution by turbulence because the tur-bulence is shown in Figures 4 and 5 to diminish during thecourse of the experiment because of the density stratificationand other modifications and transformations to the KEF inputthat are not present in the RSIF study. Therefore, it is likelythat bubble-mediated exchange plays an enhanced role in theBiosphere 2 saltwater ocean compared to the freshwatermeasurements reported by Ho et al. [2000].

4.5. Scaling of Gas Transfer to Dissipation Ratefor RainX Results

[54] Synthesizing all of these individual rain experimentsindicates that dissipation rate controls gas exchange for arain-forced system as hypothesized. According to (1), kshould scale with e

1=4 . Figure 10 shows k(600) measuredusing both ACFT and SF6 tracer release for a variety ofdifferent rain rates that include both the RainX II [see Hoet al., 2004] and RainX III [see Zappa et al., 2007] data inBiosphere 2 (rain; no wind) to be proportional to the modelexpressed in (1) with n =

1=2 . Note that in order to compareACFTand SF6 directly in Figure 10, the SF6 tracer release hasbeen adjusted to turbulence-only transfer by removing thebubble-mediated exchange (�20%) according to the esti-mates provided by Ho et al. [2000] and the discussion aboveregarding the differences in stratification and drop sizedistribution between Biosphere 2 and RSIF. The results hereclearly show that gas transfer scales with e

1=4 for this systemthat is dominated by rain and includes effects of waves andartificial background turbulence (i.e., circulation pumps).The constant of proportionality associated with (1) and used


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in Figure 10was determined by Zappa et al. [2007] to be 0.42for a wide range of measurements that included wind, wave,and tidal forcing. The e

1=4 scaling shows a higher correlation(coefficient of determination of 0.94) than would be expectedfrom the Wanninkhof [1992] quadratic wind speed parame-terization, since the process of rain and not wind is driving thenear surface turbulence that dominates the transfer. Further-more, e may prove to be more relevant than KEF in terms ofparameterizing gas transfer. The effects of stratification havebeen shown here to have a dynamic control on the nearsurface turbulence and k(600) is correlated strongly with e

1=4 .While KEF may be relevant to measure the turbulent input tothe system during rain events, e at the surface is the mostrelevant response to all themodifications and transformationsto the turbulent state that occur.

4.6. Effectiveness of ACFT in Non-Wind-ForcedConditions

[55] The direct comparison of k(600) for ACFT to SF6tracer release in Figure 10 shows that the gas transfer velocitydetermined from the ACFT and the SF6 tracer release arewithin measurement error. Similar results were found for thecomparison between k(600) determined from ACFT andatmospheric CO2 profiles in the Parker River Estuary [Zappaet al., 2003] where bed-driven turbulence dominated the gastransfer instead of the wind. Both the Biosphere 2 and ParkerRiver results provide evidence for the usefulness of ACFTunder conditions that are not those found during stronglyforced wind-driven laboratory [Atmane et al., 2004] and field[Asher et al., 2004] experiments. This discrepancy suggeststhat there is a distinct difference between the transferforced by wind and that forced by bed-generated or rain-induced turbulence, i.e., sheared versus zero-mean shearedenvironments.

4.7. Importance of Surface Dissipation Ratesin Air-Sea Gas Transfer

[56] An underlying assumption in (1) is that e is measureddirectly at the water surface. Since the profile of turbulencenear the air-water interface may be complicated by theinterplay between rain, wind, waves, current shear and otherprocesses (namely stratification), measurements at depth willnot be representative of e at the surface because the profilechanges nonlinearly with environmental forcing. The upper-most dissipation measurements during the rain experimentsat Biosphere 2 were made within a few centimeters of thesurface using the DopBeam. Figures 4 and 5 demonstrate thatthe surface turbulence is crucial to gas transfer since kH(600)tracks e (at z = 2.5 cm) regardless of the variability inturbulent dissipation rate that occurs in the bulk fluid. Thecomparison of measured and modeled k using (1) for theBiosphere 2 data show little variability in Figure 10 and evenless variability when compared to previous results [Zappaet al., 2007] across a variety of systems (i.e., estuaries, rivers,and coastal ocean) and environmental forcings (i.e., wind,wave, and tides). This small variability in Figure 10, even inthe presence of significant salinity stratification developedfrom freshwater rain on the saltwater ocean, strengthens thecase for an e

1=4 scaling. Nonetheless, some of the scatter inFigure 10 may be due to the significant spatial variability inthe rain distribution in these studies.[57] The DopBeam data shown in Figure 11 gives a profile

of dissipation rate near the air-water interface averaged overthe beginning 10 min of RE1 from Figure 4b. This profile isrepresentative of all profiles that show an e�z dependence,where z is depth positive downward. This dependence isanalogous to that suggested by Anis and Moum [1995] thathigh levels of turbulent kinetic energy at the surface, in thiscase generated directly by rain, are transported downwardaway from the surface by the motion of waves in the modelocean. Measurements of dissipation rate just below thesurface are more than an order of magnitude higher thanthose a few tens of centimeters below. Magnitudes of bulk eat Biosphere 2 have remained roughly constant during RainXII and III. The measurement of e at 25-cm depth from theDopBeam is nearly identical to that found using a single pointacoustic Doppler velocimeter (ADV) sampling at 25-cmdepth in the same model ocean under similar conditions[Ho et al., 2004].

4.8. Modeling the Near-Surface Dissipation RateProfile During Rainfall

[58] Given the importance of using the dissipation rate atthe surface for modeling gas transfer and the nonlinear near-surface profile of turbulence observed beneath rainfall thatroutinely decays by more than an order of magnitude over50 cm, modeling of this e profile will have an importantimpact on future climate studies that involve rain-induced gasexchange. The primary effect of rain falling on an open bodyof water is to impose a distributed turbulent kinetic energyflux at the surface. The subsurface turbulence generated bythe impacting droplets then diffuses downward, creating aturbulent kinetic energy (TKE) dissipation rate profile withdepth. For modeling purposes, it is assumed that any verticalcirculation induced in the water column is negligible, as isborne out by observations.

Figure 10. Gas transfer velocity from ACFT versus mod-eled k as determined from (1) for all rain rates during bothRainX II [see Ho et al., 2004] and RainX III at Biosphere 2.The gas transfer measurement using the SF6 tracer releaseduring RainX III is also shown for comparison.


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[59] A straightforward extension of themodel ofCraig andBanner [1994] is used here for the first time to model theinfluence of rainfall on the near-surface TKE budget. Thismodel was originally introduced to explore the influence ofbreaking wave turbulence on upper ocean currents. TheCraig-Banner (CB) model assumes a flat sea surface, andhorizontal momentum equations that use an eddy viscositydetermined by a Mellor-Yamada 2 1/2 turbulence scheme[Mellor and Yamada, 1982]. Here, the eddy viscosity isproportional to the mixing length and the turbulent kineticenergy, and is determined by a turbulent kinetic energyequation representing a balance between parameterized ver-sions of diffusion, dissipation and shear generation of turbu-lence. At the sea surface, we impose a surface turbulentkinetic energy input rate associated with the incident rain.[60] In the present application, the input water-side friction

velocity was set to a negligibly small level (10�5 m/s), and

the surface TKE flux, now independent of the frictionvelocity, is prescribed by the measured value. The energyand momentum diffusion coefficients Sq and Sm were set tothe standard Mellor-Yamada values of Sq = 0.20 and Sm =0.39, and the sensitivity of the results to these choices waschecked. The water-side roughness length zowas varied overthe range from 0.10 to 0.20 m, consistent with the observedturbulence penetration depth in the initial 10 min rainfallperiod before stratification effects came into play. The modeldepth was set to 200 m to simulate deep-water conditions.[61] For the given input TKE flux (KEF = 0.308 J m�2 s�1

for RE1; a small fraction is potentially lost because of theformation of the bubble cavity and is assumed to be gainedback from the turbulent wake of the bubble during thebuoyant rise to the surface (F. Veron, personal communica-tion, 2008)) and roughness length, the TKE dissipation rateprofile with depth was calculated and compared with the

Figure 11. Depth profile of dissipation rate for RE1 determined using the DopBeam directed vertically atthe surface of the model ocean in the Biosphere2 Center. The data have been averaged for roughly the first11 min in Figure 4b, and the bars denote the variability during the averaging time. The bulk rain rates aretabulated in Table 1. Because of spatial variability in the rain rate from experiment to experiment, the localdissipation rates may vary significantly. The red traces show the profile results from the Craig-Bannermodel using the measured KEF and assuming the standard Mellor-Yamada coefficients for zo values of0.15 m, 0.20 m, and 0.25 m for RE1.


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measured initial profile. The CB model results are shown inFigure 11 with the measurements of e. Figure 11 shows thatthe standard Mellor-Yamada coefficients for the imposedchoice of zo = 0.15 m provides a close agreement of the CBmodel results to the observations of e over most of theuppermost 0.5 m of the water column. The sensitivity ofthe results to different choices of zo (0.10 and 0.20 m) isindicated. Least squares regression between the CB modelresults and the measurements of turbulent dissipation rategives a slope of 1.01 for zo = 0.15 m as opposed to 1.21 and0.85 for zo = 0.10 m and 0.20 m, respectively. Furthermore,the root-mean square (RMS) difference between the CBmodelresults and the measurements of ewas 9.9� 10�5W kg�1 forzo = 0.15 m as compared to 3.0 � 10�4 W kg�1 and 1.5 �10�4 W kg�1 for zo = 0.10 m and 0.20 m, respectively. Boththe least squares regression and the RMS difference support azo = 0.15 m for this data set. The sensitivity of the modelto varying Sq and Sm was also explored. Reducing Sq byhalf required increasing zo to 0.2 m for the closest fit.Likewise, doubling Sq required decreasing zo to 0.1 m.Similar variations in Sm had minimal effect, as expected inthis quasi-static flow.[62] Gemmrich and Farmer [1999] estimate zo from pro-

files of temperature fluctuations beneath breaking waves.They used a Prandtl-type mixing model to find a linearincrease in eddy sizes with distance from the interface,resulting in a zo of 0.2 m. Effectively, this zo describes theregion near the surface that is well mixed and is similar to thenear-surface layer in the Biosphere 2 ocean. They alsoobserved that bubbles generated by breaking waves produceda layer that penetrated down to 20 cm during these samemeasurements of zo. Similarly, rain provides an input to thenear surface ocean comparable to breaking waves and thechoice of zo used in the Craig-Banner model is consistentwith Gemmrich and Farmer [1999] and with the observa-tions of the depth of stratification.[63] Thus, the exploratory efforts to use the Craig-Banner

model to infer the dissipation rate profile are very encourag-ing. This approach has the capability to account for theobserved dissipation rate profile once the KEF and zo arespecified. Prescribing the rainfall KEF alone is insufficient topredict the resulting turbulent dissipation rate near thesurface. The sensitivity of the model estimates was assessedfor a range of plausible estimates of zo using standard Sq andSm settings. It was found that the surface dissipation valueswere not very sensitive to the choice of zo, varying by lessthan a factor of 2 for a factor of 2 change in zo. Given the e

1=4

scaling in (1), an O(2) change in dissipation rate is entirelyacceptable. Therefore, the Craig-Banner model is potentiallyuseful for estimating the surface dissipation rate when thebulk epsilon and KEF are known, and for reasonable esti-mates of zo. Figure 11 shows the dissipation rate can vary atleast 2 orders of magnitude over the top 50 cm. Yet, it is thedissipation rate at the surface, and not the bulk measurement,that is crucial for estimates of air-sea gas transfer. Furtherstudy is required to refine this approach, with observations ofdissipation rate profiles and zo for different KEF rates due torain. While the exact processes that set zo are not known,stratification, drop size distribution, terminal and nontermi-nal drop velocities will all play a role. The success ofmodeling the dissipation profile during rainfall has implica-

tions for improved regional and global model predictions ofgas transfer rates and eventually of trace gas budgets.

5. Conclusions

[64] The results of the Bio2 RainX III experiment showthat near-surface turbulence is the dominant controllingfactor for the enhancement of the of gas exchange rate inthe ocean surface, even though the turbulent dissipation rateis strongly influenced by near-surface stratification. Weobserved a correlation of kH(600) with increasing rain ratefor the range of values investigated. The SF6 evasion andACFT results showing an increase in transfer velocity due torain is consistent with physical measurements made duringRainX III. Moreover, the high-resolution transfer rate andturbulence results presented here clearly show the causalrelationship between rainfall, turbulence, stratification, andair-sea gas exchange. Here, profiles of the turbulent kineticenergy dissipation rate under rainfall were measured for thefirst time during a gas exchange experiment. Stratificationmodifies and leads to the trapping of e near the surface. Thisnot only has a profound effect on the enhanced kH(600), butalso will play a role in diminishing the vertical mixing ofmass transported to the air-water interface that is important asthe driving potential in the flux of gas.[65] The results clearly show that gas transfer scales with

e1=4 for a variety of different rain rates that include both theRainX II and RainX III data in Biosphere 2 for this systemthat is dominated by rain and includes effects of waves andartificial background turbulence (i.e., circulation pumps).While KEF may be relevant to measure the turbulent inputto the system during rain events, e is the most relevantresponse to all the modifications and transformations to theturbulent state that follow. The Craig-Banner turbulencemodel, modified for rain-induced turbulence instead ofbreaking wave turbulence, bears this out and successfullypredicts the near-surface dissipation profile at the onset of therain event before stratification plays a dominant role. Thisresult has a profound impact on prediction and modeling gastransfer since it suggests that knowledge of the bulk turbu-lence and the forcing will result in the correct surface value ofe that is important to gas transfer and that is typically O(100)greater at the surface than in the bulk at a meter depth.Profiles of e are therefore required to improve our estimatesof e at the surface and gain a further understanding of theinterplay between rain, currents, wind, and waves and thetransition between various forcing regimes.[66] Although much has been learned about the influence

of rain on air-water gas exchange, most studies have focusedon laboratory or controlled experiments. It is clear that futuregas exchange experiments considering rain forcing need to beperformed in the natural environment. On the basis of thestudies presented here, we argue that more research is neededto gauge the interaction of rain with wind [Ho et al., 2007],stratification, waves [Zappa et al., 2008], and other processeson gas exchange from the open ocean to wetlands. Not untilthe mechanisms behind rain-induced gas exchange have beensufficiently understood and the process been documented innature can the ecosystem and global implications be evalu-ated. On an ecosystem scale, this would elucidate the impactof rain-induced gas exchange in quiescent environments such


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as wetlands when performing nutrient studies or determiningvolatile pollutant transport. This alsowouldmeet the growingneed among scientists to enhance our ability to determine therelative importance of the rain-induced fluxes of CO2 andother trace gases in regional and global biogeochemicalcycles.

[67] Acknowledgments. We thank S. Bissell, R. Cota, M. Hendricks,K. Mull, B. Shank, and A. Wright for their invaluable assistance during theexperiment, F. Tubiana and D. Lebel for help with data processing andanalysis, A. Jessup of the University of Washington’s Applied PhysicsLaboratory for loaning their infrared imager and CO2 laser, and B. Asherfor his thoughtful and insightful discussions on bubbles and bubble-mediated effects. This work was funded by a generous grant from theDavid and Lucile Packard Foundation and the Lamont-Doherty EarthObservatory Climate Center. Additional funding was provided by theNational Science Foundation (OCE-05-26677) and the Office of NavalResearch Young Investigator Program (N00014-04-1-0621). This is LDEOcontribution 7249.

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��M. L. Banner, W. R. McGillis, and C. J. Zappa, Lamont-Doherty Earth

Observatory, Earth Institute at Columbia University, Palisades, NY 10964,USA. ([email protected])L. F. Bliven, Laboratory for Hydrospheric Processes, NASA Goddard

Space Flight Center, Wallops Island, VA 23337, USA.J. W. H. Dacey, Biology Department, Woods Hole Oceanographic

Institution, Woods Hole, MA 02543, USA.D. T. Ho, Department of Oceanography, University of Hawai’i at Manoa,

Honolulu, HI 96822, USA.B. Ma, Electrical and Computer Engineering, Portland State University,

Portland, OR 97207, USA.J. Nystuen, Applied Physics Laboratory, University of Washington,

Seattle, WA 98105, USA.


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